面积 y=x,y=2-x,y=0

解答

面积

y = x, y = 2 - x, y = 0

1

求解步骤

要找到相交点，解

f_{i} (x) = f_{j} (x)

x = 2 - x : x = 1

x = 0 : x = 0

2 - x = 0 : x = 2

= \int_{0}^{1} ∣ f_{1} (x) - f_{3} (x) ∣ d x + \int_{1}^{2} ∣ f_{3} (x) - f_{2} (x) ∣ d x

= \int_{0}^{1} ∣ x - 0 ∣ d x + \int_{1}^{2} ∣ 0 - (2 - x) ∣ d x

\int_{0}^{1} ∣ x - 0 ∣ d x = \frac{1}{2}

\int_{1}^{2} ∣ 0 - (2 - x) ∣ d x = \frac{1}{2}

= \frac{1}{2} + \frac{1}{2}

化简

= 1

a re a y = 2 sin (x), y = e^{x}, x = 0, x = \frac{π}{2}

y^{^{'}} = x^{2} - 3 y

\int (e^{- x}) d x

x^{^{'}} = 0

\int x cos (d) x d x